"The natural distribution of prior knowledge in classrooms should not prompt abandoning instruction in grade level content, but should prompt explicit attention to connecting grade level content to content from prior learning. To do this, instruction should reflect the progressions on which the CCSSM are built. For example, the development of fluency with division using the standard algorithm in grade 6 is the occasion to surface and deal with unfinished learning with respect to place value. Much unfinished learning from earlier grades can be managed best inside grade level work when the progressions are used to understand student thinking.
"This is a basic condition of teaching and should not be ignored in the name of standards. Nearly every student has more to learn about the mathematics referenced by standards from earlier grades. Indeed, it is the nature of mathematics that much new learning is about extending knowledge from prior learning to new situations. For this reason, teachers need to understand the progressions in the standards so they can see where individual students and groups of students are coming from, and where they are heading. But progressions disappear when standards are torn out of context and taught as isolated events."
Because it takes time for students to build strong connections among mathematical ideas, they benefit from repeated and varied experiences that highlight key connections (Langrell, p. 20)
Number Talks
Number Strings
A website where teachers, coaches and mathematics educators can find new strings, post strings, get feedback on design or number choice, and discuss the pedagogy of number strings.
Talk Moves
A video from The Teaching Channel describe talk moves that encourage student participation in math discourse.
Noticing and Wondering
Video of a talk by Annie Fetter (The Math Forum) at NCTM Ignite 2011 (5 min)
Table of Contents
Essay by Phil Daro, William McCallum, and Jason Zimba posted on Tools for the Common Core
"The natural distribution of prior knowledge in classrooms should not prompt abandoning instruction in grade level content, but should prompt explicit attention to connecting grade level content to content from prior learning. To do this, instruction should reflect the progressions on which the CCSSM are built. For example, the development of fluency with division using the standard algorithm in grade 6 is the occasion to surface and deal with unfinished learning with respect to place value. Much unfinished learning from earlier grades can be managed best inside grade level work when the progressions are used to understand student thinking.
"This is a basic condition of teaching and should not be ignored in the name of standards. Nearly every student has more to learn about the mathematics referenced by standards from earlier grades. Indeed, it is the nature of mathematics that much new learning is about extending knowledge from prior learning to new situations. For this reason, teachers need to understand the progressions in the standards so they can see where individual students and groups of students are coming from, and where they are heading. But progressions disappear when standards are torn out of context and taught as isolated events."
Because it takes time for students to build strong connections among mathematical ideas, they benefit from repeated and varied experiences that highlight key connections (Langrell, p. 20)
Number Talks
Number Strings
A website where teachers, coaches and mathematics educators can find new strings, post strings, get feedback on design or number choice, and discuss the pedagogy of number strings.
Talk Moves
A video from The Teaching Channel describe talk moves that encourage student participation in math discourse.
Noticing and Wondering
Video of a talk by Annie Fetter (The Math Forum) at NCTM Ignite 2011 (5 min)
Tape Diagrams
Thinking Blocks websiteSuccess with Word Problems Using Mathematical Model Drawings